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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 4998m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4998.m1 | 4998m1 | \([1, 0, 1, -16047134, 24732961040]\) | \(1617840527930521321/623760113664\) | \(176196793423506702336\) | \([]\) | \(282240\) | \(2.8504\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4998m1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4998m do not have complex multiplication.Modular form 4998.2.a.m
sage: E.q_eigenform(10)